Which is larger: $(1.01)^{1000000}$ or $10,000$?

We can express $(1.01)^{1000000}$ as $(1 + 0.01)^{1000000}$.
Using the binomial theorem,the expansion is given by:
$(1 + 0.01)^{1000000} = \binom{1000000}{0} + \binom{1000000}{1}(0.01) + \binom{1000000}{2}(0.01)^2 + \dots + (0.01)^{1000000}$.
Considering the first two terms:
$= 1 + (1000000 \times 0.01) + \text{other positive terms}$.
$= 1 + 10000 + \text{other positive terms}$.
$= 10001 + \text{other positive terms}$.
Since all terms in the expansion are positive,it is clear that $10001 + \text{other positive terms} > 10000$.
Therefore,$(1.01)^{1000000} > 10000$.